Air currents are caused by the fact that as a planet spins on its axis, not all points on the surface move at the same angular velocity. Just as the center of a spinning record moves slower than the edge, the air above the equator moves faster than the air above regions more north or south. Because the ground itself is moving, the air currents themselves are more relative to each other than the ground, giving the effect of equatorial regions moving east to west, and non-equatorial regions moving west to east. This difference in air current causes vortexes, especially in the tropics, which are responsible for many weather patterns. This page describes the effect in more detail, including an image of the Earth's ocean air currents. Water currents also follow similar reasoning.
Further, equatorial regions are warmer, causing greater evaporation from the oceans and a drop in pressure. Water vapor, counter-intuitively, is less dense than air and therefore results in lower pressures than dry air. This contributes to the vortexes previously described, as dry air is pushed towards equatorial regions due to higher pressure.
Those basics addressed, on an aquatic world, air currents would be almost perfectly as I have described - west to east at the equator, east to west outside it, and spiraling in the tropics. If you look at the pacific in what I linked, you will see the sort of pattern you should expect on a planet with few land masses. However, since there would be nothing to determine where the vortexes start and end, as land masses generally determine that on Earth, tropical regions would be subject to sudden and intense air current (and thus weather) changes as these vortexes move around.
As a final note, axial tilt almost completely determines seasons. Elliptical orbits do not differ enough from longest to shortest to cause notable changes in temperature. The only way you could experience seasons from orbit would be if the orbit was extremely eccentric. I'm not versed well enough in astronomy to say much about that, but I suspect it would have negative consequences to life on the planet, such as possible disruption in the magnetic field.